A population of bacteria has per capita production r = 0.6, and 1.0 x 106 bacteria are added each generation.
A bacterial population that has per capita production r < 1 but that is supplemented each generation follows a discrete-time dynamical system much like that of the lungs. Use the following steps to build the discrete-time dynamical system.
a. Starting from 3.0 x 106 bacteria, find the number after reproduction.
b. Find the number after the new bacteria are added.
c. Find the discrete-time dynamical system.